• Journal for History of Mathematics
• /
• v.25 no.4
• /
• pp.37-51
• /
• 2012

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

• Earthquakes and Structures
• /
• v.17 no.5
• /
• pp.447-462
• /
• 2019

This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable's stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations.

• Publications of The Korean Astronomical Society
• /
• v.39 no.1
• /
• pp.13-26
• /
• 2024

The armillary sphere, an astronomical observation device embodying the Orbital Heaven Theory of the Later Han Dynasty in China, holds both historical and scientific significance. It has been produced in various forms by many individuals since its inception in the era of King Sejong in the Joseon Dynasty. A prominent figure in this field was Nam Byeong-cheol (南秉哲, 1817-1863), known for his work 'Uigijipseol' (儀器輯說), published in 1859, which detailed the history, production methods, and usage of the armillary sphere. This text particularly highlights 21 applications of the armillary sphere, divided into 33 measurements, covering aspects like installation, time, and positional measurements, supplemented with explanations of spherical trigonometry. Despite numerous records of the armillary sphere's design during the Joseon Dynasty, detailed usage information remains scarce. In this study, the 33 measurements described in 'Uigijipseol' (儀器輯說) were systematically classified into six for installation, nineteen for position measurement, seven for time measurement, and one for other purposes. Additionally, the measurement methods were analyzed and organized by dividing them into the ecliptic ring, moving equatorial ring, and fixed equatorial ring of the armillary sphere. In other words, from a modern astronomical perspective, the results of schematization for each step were presented by analyzing it from the viewpoint of longitude, right ascension, and solar time. Through the analysis of Nam's armillary sphere, this study not only aims to validate the restoration model of the armillary sphere but also suggests the potential for its use in basic astronomical education based on the understanding of the 19th-century Joseon armillary sphere.

• The Journal of the Acoustical Society of Korea
• /
• v.43 no.3
• /
• pp.324-334
• /
• 2024

The Wavefront Curvature Ranging (WCR) is an estimation method for a source range from the wavefront curvature of acoustic waves. The conventional method uses trigonometry to estimate the source range by assuming the sound speed as a constant. Because of this assumption, range error occurs in the ocean environment where the bottom reflection is clearly separated. In order to reduce the range error, Matched Wavefront Curvature Ranging (MWCR) was proposed applying the sound speed structure in the ocean environment and Maximum Likelihood Estimation (MLE). The range error was reduced in the results of the simulation on the proposed method. In the future, this method will be applicable to the sonar system if the reliability of ranging is confirmed by measured signal.

• The Journal of The Korea Institute of Intelligent Transport Systems
• /
• v.15 no.1
• /
• pp.66-76
• /
• 2016

Determination of type of a vehicle is being used in various areas such as collecting tolls, collecting statistical traffic data and traffic prognosis. Because most of the vehicle type classification systems depend on vehicle length indirectly or directly, highly reliable automatic vehicle length measurement system is crucial for them. This study makes use of a pencil beam laser rangemeter and devises a mechanical device which rotates the laser rangemeter. The implemented system measures the range between a point and the laser rangemeter then indicates it as a spherical coordinate. We obtain several silhouettes of cross section of the vehicle, the rate of change of the silhouettes, signs of the rates then squares the rates to apply cell averaging constant false alarm rate (CA-CFAR) technique to find out where the border is between the vehicle and the background. Using the border and trigonometry, we calculated the length of the vehicle and confirmed that the calculated vehicle length is about 94% of actual length.

• Journal of The Korean Association of Information Education
• /
• v.21 no.2
• /
• pp.199-208
• /
• 2017

The present study investigates the potential of an educational programming game as a strategy for enhancing effective domains of mathematics curriculum, which has been criticized as a problem of education in Korea. The process of programming Fortress, an educational game, in conjunction with the lesson on the trigonometric function as part of the middle school mathematics curriculum, was designed for instruction and learning, and its effectiveness was tested. The study was conducted using a nonequivalent pretest-posttest experimental design. Research procedures included the following steps: (1) both the experimental and the comparison groups participated in four classes to understand and apply the concept of the trigonometric function, and (2) the experimental group participated in Fortress game programming activities using Scratch, which was designed in this study, while the comparison group participated in solving a real-life trigonometric problem - calculating the height of a building using the concept of trigonometry. The results of the t-test showed that students' interest and perceived value of the mathematics curriculum were significantly higher in the experimental group than in the comparison group. However, the results of analysis of covariance (ANCOVA) using pretest scores of the interest and perceived value showed the influence of pretest scores on posttest scores for the interest level, although the effect of the experiment on the perceived value of the mathematics curriculum was more significant.

• Journal of the Korean GEO-environmental Society
• /
• v.17 no.3
• /
• pp.21-26
• /
• 2016

Soil particle shape analysis was conducted with sands from Jumujun, Korea and Ras Al Khair, Saudi Arabia. Two hundred times enlarged digital images of the particles of those two sands were obtained with an optical microscope. The resolution of the digital images was $640{\times}320$. By conducting digital image processing, the coordinates of the soil particle boundary were extracted. After mapping those coordinates to the complex space, Fourier transformation was performed and the coefficients of each trigonometry term were computed. The coefficients reflect the shape characteristics of the sand grains and are invariant to translation. To evaluate the shape itself excluding the size of the soil particle, the coefficient was normalized by the equivalent radius of soil particle; this is called Fourier descriptor. After analyzing the Fourier descriptors, it was found that the major characteristics of Jumunjin and Ras Al Khair sands were elongation and asymmetry. Furthermore, it was found that the particle shapes reflect the self-similar, fractal nature of the textural features. The effects of resolution on soil particle shape analysis was also studied. Regarding this, it was found that the significant Fourier descriptors were not significantly affected by the image resolution investigated in this study, but the descriptors associated with textural features were affected.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.46 no.5
• /
• pp.139-145
• /
• 2009

Recently P2P (Peer-to-Peer) networks and applications have been expanded to various field. However, because the construction of P2P network did not influence a underlying network topology or property, it may be inefficient. Especially, this inefficiency is more serious in MANET because MANET has narrow bandwidth and energy constraint. When we use a proactive routing protocol in MANET, we can know hop counts between two nodes. And, we can construct a P2P overlay network using this hop count information. However, In case of using hop count only, we can avoid a interference path selection problem and a zig-zag problem. We propose a method of improving P2P contents distribution using virtual positions. We calculate virtual positions from hop counts using the trigonometry. This method solves a interference path selection problem and a zig-zag problem. This method also allows a P2P network to influence underlying network topology. We adopt this method to a network which uses a virtual geographic routing, a proactive routing protocol, or a reactive routing protocol. We show that our proposed methods improve P2P contents distribution performance over MANET through a simulation.